The AND and OR also have slightly different meanings than in “real life”. That’s what always happens if you use natural language terms in the context of formal languages.
In English (and many other natural languages), “or” means either XOR or OR, and “and” can also mean OR in some contexts.
So it just follows that IMPLIES doesn’t mean the exact same as “implies”.
To take your example with the ravens: IMPLIES is just about whether the inputs contradict the statement. The statement “raven IMPLIES black” should be translated to “raven is black”, not “all ravens are black”, since you only ever test the statement against specific inputs.
So if you now give it “raven” and “black” as inputs, the statement is true. If you give it “dove” and “white” as inputs, it doesn’t contradict the statement, so the result is still true. Only if you give it “raven” and “white” as inputs does it contradict the statement.
Remember: Boolean logic isn’t about statements of truth, but instead as a mathematical operation. Same as you use mathematical functions and operators to “calculate x”, you also use boolean operations to calculate a result.
The AND and OR also have slightly different meanings than in “real life”. That’s what always happens if you use natural language terms in the context of formal languages.
In English (and many other natural languages), “or” means either XOR or OR, and “and” can also mean OR in some contexts.
So it just follows that IMPLIES doesn’t mean the exact same as “implies”.
To take your example with the ravens: IMPLIES is just about whether the inputs contradict the statement. The statement “raven IMPLIES black” should be translated to “raven is black”, not “all ravens are black”, since you only ever test the statement against specific inputs.
So if you now give it “raven” and “black” as inputs, the statement is true. If you give it “dove” and “white” as inputs, it doesn’t contradict the statement, so the result is still true. Only if you give it “raven” and “white” as inputs does it contradict the statement.
Remember: Boolean logic isn’t about statements of truth, but instead as a mathematical operation. Same as you use mathematical functions and operators to “calculate x”, you also use boolean operations to calculate a result.